Question:

When the velocity of projection of a body is made $n$ times, its time of flight becomes $n$ times. Range of projectile does not depend on the initial velocity of a body.

Updated On: Jul 28, 2022
  • If both assertion and reason are true and reason is the correct explanation of assertion
  • If both assertion and reason are true but reason is not the correct explanation of assertion
  • If assertion is true but reason is false
  • If both assertion and reason are false
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The Correct Option is C

Solution and Explanation

As time of flight, $T=\frac{2u \sin \theta}{g}$ $\therefore T'=\frac{2\left(nu\right) sin \theta}{g}=nT$ But range $R=\frac{u^{2} \sin 2\theta}{g}$ $\therefore R'=\frac{n^{2}u^{2} \sin 2\theta}{g}=n^{2}R.$
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Concepts Used:

Motion in a Plane

It is a vector quantity. A vector quantity is a quantity having both magnitude and direction. Speed is a scalar quantity and it is a quantity having a magnitude only. Motion in a plane is also known as motion in two dimensions. 

Equations of Plane Motion

The equations of motion in a straight line are:

v=u+at

s=ut+½ at2

v2-u2=2as

Where,

  • v = final velocity of the particle
  • u = initial velocity of the particle
  • s = displacement of the particle
  • a = acceleration of the particle
  • t = the time interval in which the particle is in consideration